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Inverse Functions

Revise Inverse Functions in Algebra for GCSE Mathematics with 8 exam-style questions and 4 flashcards. This topic appears regularly enough that it should be part of a solid GCSE revision cycle.

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Functions as Machines

Introduction 2

Key Facts

Key Facts 3

Method: Finding an Inverse Function

Deep Dive 4

Worked Example 1: Finding an Inverse

Notes 5

Worked Example 2: Verifying an Inverse

Notes 6

Common Mistakes to Avoid

Exam Tips 7

Knowledge Organiser: Inverse Functions

Summary

Sample Flashcards

What is an inverse function?

A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)

What does f⁻¹ notation mean?

Inverse function (NOT 1/f). It's the function that undoes f, not the reciprocal

Exam questions for Inverse Functions

What does f⁻¹(x) represent?

A. The reciprocal of f(x), i.e. 1/f(x)
B. The function that undoes f(x)
C. The square of f(x)
D. The negative of f(x)

1 markfoundation

Explain why the function f(x) = x² (for all real x) does not have an inverse function over its full domain.

2 markshigher

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